Rigid aircraft motion while airborne is described by complex six degrees of freedom (6-DOF) dynamics. An aircraft, while in the air, is free to move in six degrees of freedom. The aircraft can rotate about any of its three axes x, y and z. The corresponding rotational or angular velocities are labeled as p (roll rate), q (pitch rate) and r (yaw rate), respectively. The aircraft can also translate along any of its three axes x, y, and z. The corresponding translational or linear velocities are identified as u (forward velocity), v (side velocity) and w (up or down velocity), respectively.
Rotational and translational aircraft motion along these axes is determined by measurement or calculation based on measured data reflecting angular and linear aircraft movement. Aircraft position, speed and acceleration (or load factor) data measured from different instruments usually contain measurement errors from sensors, transducers or data acquisition systems. In order to obtain accurate aircraft flight data, a kinematic consistency process is used to remove measurement errors. Kinematics relates to the motion of a body or a system of bodies without consideration given to its mass or the forces acting on it. Kinematic consistency is a process by which aircraft dynamic data measured and recorded in a flight test or in a Flight Data Recorder (FDR) is kinematically corrected in accordance with physics laws. Kinematically corrected flight test data is essential for aerodynamic coefficient extraction and subsequent simulation model development. Kinematic checking of FDR data provides accurate aircraft motion information for accident and incident investigation.
Rotational Kinematic Consistency Analysis
Flight test and FDR data record Euler angles for bank φF, pitch θF and heading ΨF. This information is typically determined using an onboard aircraft computer such as in an Inertial Reference Unit (IRU). Rotational kinematic consistency procedures use these Euler angles to calculate angular accelerations pdt, qdt, rdt and angular rates p, q, r.
The rates of Euler angles are calculated by differentiating the recorded Euler angles. Aircraft angular roll p, pitch q and yaw r rates are calculated through transformation. The resulting angular rates produce spiky data due to sparse and/or noisy data initially incorporated in the Euler angles. The angular rates must be filtered to mask off the high frequency component of the data. This filtering process is based on an artificially established threshold that is subjectively determined and variable in nature. As such, in addition to limitations associated with its subjective implementation, it inherently generates errors that can cumulate when integrated for Euler angles, and can also introduce artificial oscillations not present in the original data. Angular accelerations pdt, qdt, rdt are calculated by differentiating angular roll p, pitch q and yaw r rates.
Translational Kinematic Consistency Analysis
Flight test and FDR data produce load factors measured by aircraft accelerometers. Load factor components include longitudinal acceleration (x-axis), lateral acceleration (y-axis) and normal or vertical acceleration (z-axis). Load factors are useful parameters because when integrated properly they provide information about the inertial velocity and position of the aircraft. In addition, this information may be used with airspeed information to calculate winds. However, accelerometers that measure the load factors suffer from inherent errors that must be corrected to avoid misleading results due to integrations.
Two principal accelerometer errors are (1) the error due to the accelerometer location not coinciding exactly with the center of gravity (CG), and (2) the error due to accelerometer offsets or biases. The magnitude of the error due to the accelerometer location not coinciding with the CG is typically small, but may be significant. The bias error, on the other hand, is likely very significant because even a small offset will generate large errors when integrated over time. The load factors reported by the accelerometers are rarely the actual load factors at the accelerometer location because the sensor is not calibrated perfectly. The recorded load factor at the accelerometer is often offset from the true value by a constant bias. The biases that apply to an upset event must be determined at a point prior to but as close to the upset event as possible. The biases must be accounted for because even small errors in load factor data will produce very large errors in speed and position calculations when integrated over time.
Various approaches have been developed for removing accelerometer bias error. One method of performing kinematic consistency processing is to simplify dynamics by ignoring 6-DOF coupling or, in other words, ignoring the rotational velocities p, q and r and the translational velocities u, v and w. While this approach can avoid difficulties in dealing with 6-DOF dynamics complexities, it produces kinematic correction only for trimmed level flight. For flight maneuvers such as banked turns and stalls the method fails to produce a reliable and consistent correction for the entire maneuver. For the same reason the method is also not adequate for analyzing FDR data recorded during aircraft accidents/incidents.
Under ideal circumstances, the 6-DOFs are coupled when aircraft flight data is evaluated to provide optimum results. A different method of performing kinematic consistency processing that preserves that 6-DOF dynamics is that used by the National Transportation Safety Board (NTSB) in association with the analysis of FDR data for aircraft accident/incident investigations.
In the NTSB method, accelerometer biases are calculated for the aircraft in flight through an iterative process that compares the position resulting from integration of the accelerometer data with a position calculated using recorded navigation data. First, the actual position of the aircraft is defined using groundspeed and drift angle navigation information recorded by the FDR. A better estimate of altitude is also made by solving the hydrostatic equation with estimates of the actual air density at each point. Next, an estimate of the accelerometer biases is made by computing the load factors that result from the position information just derived, and comparing these to the recorded load factors.
At this point the iteration begins. The load factors are updated with the bias estimates, and then integrated to obtain position information. These integrated positions are compared to the inertial positions calculated previously, and an error is calculated. The sensitivity of the position error to each of the accelerometer biases is calculated by changing the bias values slightly and recomputing the errors. Using these sensitivities, the biases are updated, and the positions, errors and biases are recalculated. When changes in the biases no longer result in a reduction in the errors, then the best estimate of the biases has been found and the final load factors are computed. The final integrated velocities and positions are also calculated and represent the best available estimate of the inertial speeds.
The NTSB approach relies heavily on trial-by-error iteration and the subjective efforts of data manipulators to manually remove accelerometer bias error based on experience and individual interpretation. For example, NTSB process is laborious and not repeatable with different users because each user must rely on subjective judgment to modify the bias error during the iterative process. This approach magnifies computational difficulties associated with equation couplings and integration. Moreover, because the approach relies heavily on subjective experience, the accuracy and reliability of data correction are significantly diminished. In addition, with the NTSB process, it is mathematically difficult to reconstruct time-varying load factors if less than the basic required linear data is available.
Wind Analysis
Wind is the difference between the motion of an aircraft relative to the Earth and its motion relative to the air. Determining wind speed and direction is an aspect of aircraft flight analysis that is important both for simulation model development as well as for accident and incident investigation. The accuracy of current wind analyses is suboptimal due to their reliance on the results of inferior rotational and translational kinematic consistency analyses, as described above. In addition, current wind analyses do not accurately evaluate the impact of aircraft sideslip.
Thus, there is a need for an automated kinematic consistency process that overcomes the limitations associated with current rotational and translational kinematic consistency processes and wind analyses.